Question

in triangle abc if angle a = 90° , angle b = 48° . find angle c​

Answer 1

★ Given :-

In triangle abc,

• ∠a = 90°
• ∠b = 48°

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★ To Find :-

The ∠c in a triangle

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★ Used Formula :-

$\bf \red{\implies Sum \: of \: all \: angles \: _{(Triangle)} = 180°}$

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★ Solution :-

In triangle abc,

• ∠a = 90°
• ∠b = 48°

Let,

• ∠c = x

We know that,

$\bf \implies Sum \: of \: all \: angles \: _{(Triangle)} = 180°$

So,

$\bf \implies \angle a + \angle \: b \: + \angle \: c \: = 180°$

$\bf \implies 90° + 48° + x= 180°$

$\bf \implies 138° + x= 180°$

$\bf \implies x= 180°- 138°$

$\red{\implies \underline{ \boxed{ \bf x= 42°}}}$

Hence,

∴ ∠c = 42°

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★ Verification :-

$\bf \implies Sum \: of \: all \: angles \: _{(Triangle)} = 180°$

$\bf \implies \angle a + \angle \: b \: + \angle \: c \: = 180°$

We know that,

• ∠a = 90°
• ∠b = 48°
• ∠c = 42°

So,

Take 42° instead of x

Here,

$\bf \implies 90° + 48° + 42°= 180°$

$\bf \implies \boxed{ \bf180°= 180° }$

Hence, verified !

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Answer 2

Answer:

The measure of ∠$c$ is $42^{0}$.

Step-by-step explanation:

Given : In a Δ$abc$, the ∠$a=90^{0}$

                                  ∠$b=48^{0}$

To find : Measure of ∠$c$ =?  

Solution :

• It is given that, In a Δ$abc$, the ∠$a=90^{0}$

                                  ∠$b=48^{0}$

• We have to find the measure of ∠$c$.
• We know that, in a triangle, the sum of all angles in a triangle is $180^{0}$.
• According to this condition, in a Δ$abc$, we have  

            ∠$a$+∠$b$+∠$c=180^{0}$

• Put values of ∠$a=90^{0}$ and ∠$b=48^{0}$, we get

                  ∴ $90^{0} +48^{0} +$∠$c=180^{0}$

                         ∴ $138^{0}$$+$∠$c=180^{0}$

• Transpose $138^{0}$ to other side, we get

                                ∴ ∠$c=180^{0}$$-138^{0}$

                                  ∴ ∠$c$ $= 42^{0}$

• ∴ The measure of ∠$c$ is $42^{0}$.